Bifurcation structures and transient chaos in a four-dimensional Chua model
TLDR
In this article, a four-dimensional four-parameter Chua model with cubic nonlinearity was studied applying numerical continuation and numerical solutions methods, and the bifurcation curves of the model were obtained with the possibility to describe the shrimp-shaped domains and their endoskeletons.About:
This article is published in Physics Letters A.The article was published on 2014-01-10 and is currently open access. It has received 42 citations till now. The article focuses on the topics: Saddle-node bifurcation & Bifurcation diagram.read more
Citations
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Journal ArticleDOI
Distribution of chaos and periodic spikes in a three-cell population model of cancer
TL;DR: A wide-ranging systematic numerical classification of the oscillatory states and of their relative abundance of cell populations is reported, characterized here by two independent and complementary types of stability diagrams: Lyapunov and isospike diagrams.
Journal ArticleDOI
Numerical bifurcation analysis of two coupled FitzHugh-Nagumo oscillators
TL;DR: The behavior of neurons can be modeled by the FitzHugh-Nagumo oscillator model, consisting of two nonlinear differential equations, which simulates the behavior of nerve impulse conduction through the neuronal membrane as discussed by the authors.
Journal ArticleDOI
Crisis and inverse crisis route to chaos in a new 3-D chaotic system with saddle, saddle foci and stable node foci nature of equilibria
TL;DR: In this article, a 3D autonomous chaotic system with three different natures of equilibria, namely saddle, saddle foci and stable node foci, has been proposed.
Journal ArticleDOI
Periodic oscillations of the forced Brusselator
TL;DR: In this paper, the authors study the organization of stability phases in the control parameter space of a periodically driven Brusselator and report high-resolution stability diagrams classifying periodic phases in terms of the number of spikes per period of their regular oscillations.
Book ChapterDOI
Spiking Systematics in Some CO2 Laser Models
TL;DR: In this paper, the authors review recent progress in the classification of laser spiking, periodic or nonperiodic self-pulsations, predicted for CO 2 lasers with modulated parameters and with feedback, instantaneous or delayed.
References
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Determining Lyapunov exponents from a time series
TL;DR: In this article, the authors present the first algorithms that allow the estimation of non-negative Lyapunov exponents from an experimental time series, which provide a qualitative and quantitative characterization of dynamical behavior.
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MATCONT: A MATLAB package for numerical bifurcation analysis of ODEs
TL;DR: The sparsity of the discretized systems for the computation of limit cycles and their bifurcation points is exploited by using the standard Matlab sparse matrix methods.
Book
Transient Chaos: Complex Dynamics on Finite Time Scales
Ying-Cheng Lai,Tamás Tél +1 more
TL;DR: In this article, the transition from classical chaotic scattering to transient chaos is discussed in high dimensions and fractal basin boundary boundaries, and passive and active processes in open Chaotic Flows are discussed.
Journal ArticleDOI
Bifurcation phenomena near homoclinic systems: A two-parameter analysis
TL;DR: In this article, the bifurcations of periodic orbits in a class of autonomous three-variable, nonlinear-differential-equation systems possessing a homoclinic orbit associated with a saddle focus with eigenvalues (ρ ±iω,λ), where ¦ρ/λ¦ < 1 (Sil'nikov's condition), are studied in a two-parameter space.
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From High Dimensional Chaos to Stable Periodic Orbits: The Structure of Parameter Space
TL;DR: In this paper, the fundamental structure of these windows is described, and under what circumstances one can expect to find them in higher dimensional chaotic systems, and the results are applicable to systems that exhibit several positive Lyapunov exponents.